Radiographic imaging, in its simplest expression, is an X-ray beam traversing an object and a detector relating the overall attenuation per ray. The attenuation is derived from a comparison of the same ray with and without the presence of the object. From this conceptual definition, several steps are required to properly construct an image. For instance, the finite size of the X-ray generator, the nature and shape of the filter blocking the very low energy X-ray from the generator, the details of the geometry and characteristics of the detector, and the capacity of the acquisition system are all elements that affect how the actual reconstruction is performed. In the reconstruction, the map of the linear attenuation coefficient (LAC) of the imaged subjects is obtained from the line integrals of the LAC through an inverse Radon transform. The line integrals can be related to the logarithm of the primary intensity of the X-rays passing through the subject.
A third-generation CT system can include sparsely distributed fourth-generation, photon-counting detectors. In such a combined system, the fourth-generation detectors collect primary beams through a range of detector fan angles.
In spectral CT, with combined 3rd- and 4th-generation geometries, two datasets from the 3rd- and 4th-generation detectors having different numbers of projection views are involved in the reconstruction problem. No methods are known for using the ordered subsets (OS) methodology for this specific reconstruction problem. The conventional OS scheme cannot be directly applied to this spectral CT reconstruction problem to gain speedup because two sets of data having different numbers of projection views are involved, one set containing a sparse number of views and the other set containing a dense number of views.